Simplify the following expression: $p = \dfrac{q^2 + 16q + 63}{q + 7} $
Solution: First factor the polynomial in the numerator. $ q^2 + 16q + 63 = (q + 7)(q + 9) $ So we can rewrite the expression as: $p = \dfrac{(q + 7)(q + 9)}{q + 7} $ We can divide the numerator and denominator by $(q + 7)$ on condition that $q \neq -7$ Therefore $p = q + 9; q \neq -7$